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1 Government Debt Management: the Long and the Short of it E. Faraglia (U. of Cambridge and CEPR) A. Marcet (IAE, UAB, ICREA, BGSE, MOVE and CEPR), R. Oikonomou (U.C. Louvain) A. Scott (LBS and CEPR) () Government Debt Management 1 / 32

2 Motivation Understand some facts of debt management practice in the US in an environment that features: Fiscal policy and debt management are jointly modelled; Ramsey planner with full commitment; () Government Debt Management 2 / 32

3 Motivation Angeletos (2002) Buera and Nicolini (2004) (ABN) study debt management in an economy with effectively complete markets: They find 1 The optimal portfolio is to issue long term bonds and hold short term savings 2 Positions are several multiples of GDP; 3 Optimal Tax smoothing. 1. and 2. seem a problem, very distant from the data. () Government Debt Management 3 / 32

4 Data: Share of Short Term Debt in the US () Government Debt Management 4 / 32

5 Data: US ( ) The share of short term debt is sizeable : 36% on average; Positions are not large multiples of GDP; The shares is persistent and exhibit low volatility: First order autocorrelation of short bond is 0.96; the Standard deviation is 0.059; The portfolio shares are never zero or "negative"; () Government Debt Management 5 / 32

6 In addition, if markets are effectively complete, debt has same persistence as ouptut debt co-moves negatively with primary deficit Very much unlike the data. But introducing incomplete markets matches the data. (Marcet and Scott (2009)) () Government Debt Management 6 / 32

7 When is optimal debt management closer to observed? Nosbusch (2008) Lustig, Sleet and Yeltekin (2008) Both assume multiple bonds, effectively INcomplete markets, and no lending constraints They find size of positions is reasonable, but all debt should be long term. They solve problem 2. but not problem 1. () Government Debt Management 7 / 32

8 This Paper Look for a "minimal" amount of frictions to be imposed so optimal debt management is closer to the data. Ramsey equilibrium; Government can only use only 2 bonds: a one-period and N-period bonds; Can be seen as: Introduce a long bond in Aiyagari, Marcet, Sargent and Seppälä (2002) or Introduce "true" market incompleteness in ABN. () Government Debt Management 8 / 32

10 Summary of the Results No buyback is essential to explain the coexistence of short and long debt/savings: long bonds are still used for their fiscal insurance properties; but under no buyback long bonds create N period cycles in taxes short bonds help smooth taxes. No buyback and coupons match some observed moments much better The results are robust to introducing callable bonds. () Government Debt Management 10 / 32

15 Computational Issues "Condensed PEA" In case of a large number of state variables global approximation methods can become really diffi cult to solve: curse of dimensionality. the idea of this approach is To approximate E t (u c,t+n ) = Θ (s t ) 1. Choose a subset of state variables ("core") 2. Use PEA to get a first approximation of the model 3. Check if the rest of the state space that we have discarded improves the approximation of the model. 4. If so choose linear combination of "non-core" with highest predictive power, add one this as a new extra state variable. 5. Do this until you do not improve any longer the approximation () Government Debt Management 15 / 32

19 Share of short term debt S t US DATA BuyBack Lending No Lending E (S t ) 36% -272% 26% σ St corr(s t, S t 1 ) corr(mvt S t L ) Model: Average of 1000 samples of 60 periods In the no lending model we get a lot of periods in which short term bond is 0 (8% of all periods in our simulation). 40% of the time we have an average share that is below 20% (in the data short term debt is never below 26%). () Government Debt Management 20 / 32

20 Buyback Model: Moments Can be described as adding many possible realizations of g to ABN Model with no lending, b 1,t 0 and b N,t 0. a multi-period version of Nosbusch (2008) a version of Lustig et al. (2008) but with real debt, without nominal rigidities and fewer bonds than realizations of g () Government Debt Management 19 / 32

21 Figure 4: Optimal Portfolio under Buyback - Lending Model Short Bond Long Bond Bonds Period Notes: The Figure plots a sample path of the optimal portfolio under buyback. The bounds (upper and lower) correspond to 150% of (steady state) GDP. The solid line represents the short term bond. The dashed line the long maturity bond. 44

22 Figure 6: Optimal Portfolio under Buyback - No Lending Model Short Bond Long Bond Bonds Period Notes: The Figure plots a sample path of the optimal portfolio under buyback and No Lending. The upper bound is 150% of (steady state) GDP. The solid line represents the short term bond. The dashed line the long maturity bond. 46

23 Share of short term debt S t US DATA BuyBack Lending No Lending E (S t ) 36% -272% 26% σ St corr(s t, S t 1 ) corr(mvt S t L ) Model: Average of 1000 samples of 60 periods In the no lending model we get a lot of periods in which short term bond is 0 (8% of all periods in our simulation). 40% of the time we have an average share that is below 20% (in the data short term debt is never below 26%). () Government Debt Management 20 / 32

24 Data: Total Issuance () Government Debt Management 21 / 32

25 Data: BuyBacks From 1920 to 2011 the government has redeemed 96% of debt at redemption date or within a year to it. () Government Debt Management 22 / 32

26 The no Buyback Assumption Under complete markets, buyback or no buyback do not matter ABN, Nosbusch, Lustig et al. all assume buyback Under incomplete markets the assumption matters () Government Debt Management 23 / 32

27 Model with No Buyback and one Long Bond Assume government would only issue one long bond. Then the budget constraint such that: g t + b N,t N = τ t (T x t ) + p N,t b N,t β jn u c,t+nj (τ u t+nj l t+nj g t+nj ) = b N,t N for every t j=0 c,t If g 0 > g t = g for t 1 then τ 0 and b N,0 will increase. I have to redeem the bond in t + N by rising taxes and more debt. Can t do anything in the middle. There is an N period cycle in fiscal policy which violates tax smoothing. () Government Debt Management 24 / 32

28 Taxes and No Buyback only one long bond () Government Debt Management 25 / 32

35 Bond Term (in years) Call Window* (in years) Notes: The table shows the call windows (maturity minus first possible call date) for callable bonds in the US. The data are extracted from the CRSP and refer to government debt issued since the 1940s. Table 5: Bond Terms and Call Windows 40

36 Figure 15: Callable Bonds over Long Bonds in the US data Normalized Count [%] Bonds with 2 year call window Normalized Count [%] Bonds with 3 year call window Normalized Count [%] Normalized Count [%] Bonds with 4 year call window Bonds with 5 year call window Notes: The plots shows the timing of redemptions of callable debt in the US for all callable securities between The top left shows the timing for bonds whose first call date is 2 years before maturity, the top right 3 years, and the bottom panels 4 and 5 years. 55

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